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Unformatted text preview: Homework 1 solutions CE 93, Spring 2011 (Prof. Walker) Problem 1: Gamma (Densities) Histogram: Using the square route law, m=sqrt(38)~6. However, using the default value of 10 equal bins makes the data visibly easier to interpret as we can see more precisely around which values the data actually clusters around. 2410 2420 2430 2440 2450 2460 2470 2480 2490 2 4 6 8 10 12 2410 2420 2430 2440 2450 2460 2470 2480 2490 1 2 3 4 5 6 7 8 9 gamma The values of gamma range from 2415 to 2488, with median being 2445.5. Observations are concentrated between 2430 and 2460. The dataset is somewhat skewed to the right, since it has a slightly longer tail to the right. Frequency diagram: It follows the same shape as the corresponding histogram. Normalized frequency diagram: It can be observed that, with equal widths of bins, the normalized frequency diagram and the frequency diagram have the same shape, but with different scales. In frequency diagram, the sum of bar heights is equal to 1, whereas in the normalized frequency diagram the bar areas add up to 1. 2410 2420 2430 2440 2450 2460 2470 2480 2490 0.05 0.1 0.15 0.2 0.25 Frequency (Total:38) gamma 2410 2420 2430 2440 2450 2460 2470 2480 2490 0.005 0.01 0.015 0.02 0.025 0.03 0.035 Normalized Frequency (Total:38) gamma Normalized frequency polygon diagram: Unequal bins (there is no unique solution for this part. As long as students make reasonable judgments and description, they should get the credits)....
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 Spring '08
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